A Study Path for Mathematics, Statistics, and Programming in Quant Finance

# Self study references for a Mathematician


# Self study references for a Mathematician












I just finished my undergraduate (BSc) degree in Pure Mathematics & Applied Mathematics. I am starting my postgraduate degree in Pure Mathematics in a month's time.

I am considering pursuing a career in Quantitative Finance when I have finished my studies, but I will have to self-study a lot of the work myself since my Mathematical education will be mostly purely theoretically based.

Are there any recommendations of books that I can obtain to self-study some of the necessary mathematics and statistics/applications that I will be required to know as a quant?

## Answer by hjs (score 14)

https://quant.stackexchange.com/a/22994

In general, quantitative finance requires mathematics, finance, and numerical programming. The mix of the three and the areas of focus within the three will depend on the particular area you intend to work in. For example, option pricing, risk, and asset management are all related but derivative modeling would draw more on stochastic processes and martingales, whereas risk and asset management would draw more on statistics.

For the programming side, it's good to be familiar with numerical libraries like Lapack, numerical programming languages like Matlab, and source control (git). Programming in Python, C and C++ is a good idea too, as well as some reasonable level of computer science & software engineering (data structures, algorithms, software design, etc).

To start, one should at least have some familiarity with numerical methods, such as from:

- Press, Teukolsky, Vetterling & Flannery, Numerical Recipes

but be warned that Numerical Recipes can be simplistic.

For option pricing and the mathematically sophisticated, it helps to have a strong background in probability and measure theory. For that, the following texts would be useful:

- Billingsley, Probability and Measure

- Williams, Probability and Martingales

- Halmos, Measure Theory

For the basics of options, everyone uses:

- Hull, Options, Futures and Other Derivatives

but I preferred:

- Cox & Rubinstein, Options Markets

when I was first learning the subject. But, Cox & Rubinstein is old, and Hull is regularly updated.

That will give you the basics on the finance side in an intuitive way but not in a mathematically rigorous way. For the mathematical rigor, I recommend:

- Steele, Stochastic Calculus and Financial Applications.

Steele rigorously develops stochastic processes, martingales, Ito integration in a financial context but includes the intuition, so he's also being very down to earth and concrete.

Other general, texts a little more sophisticated than Hull, but less rigorous than Steele that people commonly like would include:

- Baxter & Rennie, Financial Calculus: An Introduction to Derivative Pricing

- Shreve, Stochastic Calculus for Finance I: The Binomial Asset Pricing Model

- Shreve, Stochastic Calculus for Finance II: Continuous-Time Models

After that, there are lots of different places to go. It will depend on the numerical methods needed, the asset class being worked on, etc.

For example, for more on the numerical methods and the PDE approaches, there's:

- Wilmott, Dewynne & Howison, Option Pricing: Mathematical models and computation

Every interest rate derivative quant needs to be familiar with:

- Brigo & Mercurio, Interest Rate models - Theory and Practice

For other areas, the list would be different.

## Answer by Gordon (score 3)

https://quant.stackexchange.com/a/22989

For general mathematical finance, you may start with the book Stochastic Calculus for Finance, and then the books Martingale Methods in Financial Modelling and Mathematical Methods for Financial Markets.

After those preparations, you can start with some books in specialized areas such as the books Interest Rate Models by Brigo and Mercurio, Credit Risk by Bielecki and Rutkowski, and Counterparty Credit Risk by Brigo et al. Some other numerical computation and programming skills are also needed.

## Answer by Neeraj (score 2)

https://quant.stackexchange.com/a/22991

As you don't have any background in finance. I would recommend you following book :

- Investment by Bodie

- Options, Futures, and Other Derivatives by Hull

- An Introduction to the Mathematics of Financial Derivatives by Neftci



After reading these books you can easily move to high level books as pointed by Gordon.

Some auxiliary book that might help you to get better understanding are :

- Analysis of Financial Time Series by Tsay

- Essentials of Econometrics by Damodar Gujarati and Dawn Porter

## Answer by Tim  (score 1)

https://quant.stackexchange.com/a/22950

In the case you're interested in asset management, Robbert Shiller's open fiance course is definitely a good introduction to finance, although not quantitative. In addition to that, John Cochrane's course on Coursera is a very good. Here portfolio theory and option pricing is approached from a quantitative perspective.